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Plzz help me with this trig proof ​

Plzz help me with this trig proof ​-example-1

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Answer:

Explanation:


(sin3A)/(cosA) + (cos3A)/(sinA)


(sin3AsinA)/(sinAcosA) + (cos3AcosA)/(sinAcosA)


(cos3AcosA + sin3AsinA)/(sinAcosA)

From here, remember the following identity:


cos(X - Y) = cosXcosY + sinXsinY

If we set
X = 3A and
Y = A, we get the following:


cos(3A - A) = cos2A = cos3AcosA + sin3AsinA

we can then plug this back into our original equation:


(cos2A)/(sinAcosA)

From here, remember the following identity:


cos2A = cos^(2)A - sin^(2)A

we can then plug this back into our original equation:


(cos^(2)A - sin^(2)A)/(sinAcosA)


(cos^(2)A)/(sinAcosA) - (sin^(2)A)/(sinAcosA)


(cosA)/(sinA) - (sinA)/(cosA)


cotA - tanA

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